The Francona Factor was at work again Wednesday as the Indians officially signed free agent pitcher Daisuke Matsuzaka.

The 32-year-old right-hander signed a minor-league contract with the Tribe. He is in the team's major-league training camp as a non-roster player. He is one of seven pitchers vying for two openings in the Indians' starting rotation.

If Matsuzaka wins one of those rotation spots, he will be paid $1.5 million this year. If he reaches various incentives, the value of the contract could go as high as $4 million.

Matsuzaka spent the first five of his six years with the Red Sox pitching for Tribe manager Terry Francona, when Francona was the manager in Boston.

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Speaking to reporters through an interpreter at his introductory news conference at the Indians' spring training camp in Goodyear, Ariz., Matsuzaka gave his reasons for signing with Cleveland.

"I talked to a few teams," he said. "It came down to I wanted to pitch for an American League team and wanted to pitch against Boston to see what that would be like. And I wanted to play under Tito again. Seeing his smile brings a calm to me."

Matsuzaka threw his first bullpen session Wednesday.

"For his first pen, he looked crisp, and he showed good maturity. He wasn't just out there letting it fly," said Francona. "He looked in really good shape and looked like he was healthy, which is good. But it's his first pen. We don't want to start evaluating people yet."

Matsuzaka's career in Boston ran the gamut. In 2008, he was 18-3 with a 2.90 ERA and finished fourth in the voting for the Cy Young Award. In 2011 he had Tommy John surgery, and in 2012 he struggled through 11 starts, going 1-7 with an 8.28 ERA.

"We want him to come in here and be Dice-K," said Francona. "I saw him the first day he came (to this country). I have a long history with him. He knows how to win. He's been a high profile, big winner not only in Japan but here."

Francona said he expects to see Matsuzaka make a major progression this year in his continued rehab from Tommy John surgery.

"A lot of times it's not until the second year back from Tommy John that you get the chance to see the guy you want to see," Francona said. "The first year back is tough. Guys do it and they pitch. But all of a sudden you get another year removed from the surgery and you start to see the guy that was there before (the surgery). With Dice-K, there's a lot to like in what was there before."

Indians general manager Chris Antonetti said the hopes for Matsuzaka this spring aren't real complicated.

"Most importantly we want to see that he's healthy, and he's able to go through spring training and demonstrate the stuff we've seen from him in the past," said Antonetti. "Obviously he's had a long and distinguished record, and when he's healthy he's been a very good pitcher here, and in Japan."

Matsuzaka will compete with Zach McAllister, Corey Kluber, Carlos Carrasco, David Huff, Trevor Bauer and Scott Kazmir for the two open spots in the Tribe's rotation.

"We will have a lot of competition for those last couple spots in the rotation," said Antonetti. "We will go with the starters who give us best chance to win."